Galileon Duality

TL;DR

The paper demonstrates a duality in Galileon theories where a free scalar field corresponds to a higher-order Galileon, showing superluminal propagation can coexist with causality and revealing new insights into their strong and weak coupling regimes.

Contribution

It introduces a dual formulation of Galileon theories, linking free scalar fields to higher-order Galileons and exploring implications for causality and the Vainshtein mechanism.

Findings

Duality maps free scalar fields to higher-order Galileons.

Superluminal propagation does not violate causality or the S-matrix.

Duality exchanges strong and weak coupling regimes for point sources.

Abstract

We show that every Galileon theory admits a dual formulation as a Galileon theory with new operator coefficients. In n dimensions a free scalar field in Minkowski spacetime is dual to a (n+1)-th order Galileon theory which exhibits the Vainshtein mechanism when coupled to sources and superluminal propagation even on-shell. This demonstrates that superluminal propagation is compatible with an analytic S-matrix and causality. For point sources, the duality interchanges the strongly coupled Vainshtein regime with the weakly coupled asymptotic regime. The duality is made manifest in the context of the decoupling limit of bigravity, but is independent of this.